Exercise 6

# Exercise 6 - University of California Department of...

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University of California D. Steigerwald Department of Economics Economics 140A Exercise 6 1. Assume the population regression model is (1) t * t * t U X Y where all variables are expressed as deviations from their respective sample means. Let B be the OLS estimator of . Additionally, assume that the variable Y t , rather than * t Y , is obtained in the measurement process. We assume that (2) Yt * t t V Y Y where   . V , X Cov Yt * t 0 a) If we estimate (1) using Y t instead of * t Y , is B unbiased? If not, on what will the bias depend? How will this change the error variance, and how will it affect tests of null hypotheses concerning ? b) Now assume that * t Y is correctly measured, but that * t X is measured with error. That is, assume that we obtain (3) Xt * t t V X X where * t X is the true value and X t is the observed value. Further, assume that   . V , X Cov Xt * t 0 The model we estimate is (4) . U X Y t t * t I s B

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Exercise 6 - University of California Department of...

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